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Mathematics

Find the equation of the line passing through the point (1, 4) and intersecting the line x - 2y - 11 = 0 on the y-axis.

Straight Line Eq

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Answer

Since line x - 2y - 11 = 0 intersects y-axis, the point where it will intersect there x-coordinate = 0.

So, putting x = 0 in equation,

⇒ 0 - 2y - 11 = 0
⇒ -2y = 11
⇒ y = -112\dfrac{11}{2}

Coordinates = (0,−112)\Big(0, -\dfrac{11}{2}\Big)

So, the line passes through (1, 4) and (0,−112)\Big(0, -\dfrac{11}{2}\Big).

The equation of the line joining two points is given by,

y−y1=y2−y1x2−x1(x−x1)y - y1 = \dfrac{y2 - y1}{x2 - x1}(x - x1)

Putting values we get,

⇒y−4=−112−40−1(x−1)⇒y−4=−11−82−1(x−1)⇒y−4=192(x−1)⇒2(y−4)=19(x−1)⇒2y−8=19x−19⇒19x−2y−19+8=0⇒19x−2y−11=0.\Rightarrow y - 4 = \dfrac{-\dfrac{11}{2} - 4}{0 - 1}(x - 1) \\[1em] \Rightarrow y - 4 = \dfrac{\dfrac{-11 - 8}{2}}{-1}(x - 1) \\[1em] \Rightarrow y - 4 = \dfrac{19}{2}(x - 1) \\[1em] \Rightarrow 2(y - 4) = 19(x - 1) \\[1em] \Rightarrow 2y - 8 = 19x - 19 \\[1em] \Rightarrow 19x - 2y - 19 + 8 = 0 \\[1em] \Rightarrow 19x - 2y - 11 = 0.

Hence, equation of line is 19x - 2y - 11 = 0.

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